Reservoir computing using passive optical systems

ABSTRACT

A method comprising providing an input signal to at least one input node of a computing reservoir by temporally encoding the input signal by modulating the at least one photonic wave as function of the input signal is described. The method further comprises propagating the at least one photonic wave via passive guided or unguided propagation between discrete nodes of the computing reservoir, in which each discrete node is adapted for passively relaying the at least one photonic wave over the passive interconnections connected thereto. The method also comprises obtaining a plurality of readout signals, in which each readout signal is determined by a non-linear relation to the at least one photonic wave in at least one readout node of the computing reservoir, and combining this plurality of readout signals into an output signal by taking into account a plurality of training parameters.

FIELD OF THE INVENTION

The invention relates to the field of information processing and machinelearning. More specifically it relates to systems and methods forreservoir computing using passive optical systems.

BACKGROUND OF THE INVENTION

Nowadays, when one can easily be swamped with data, the relevantquestion in many applications is no longer how to acquire data, but howto extract the most relevant information from it. Machine learning is aresearch field dealing with this kind of information processing, and anew paradigm from that field that gained a lot of popularity isReservoir Computing (RC). The present invention relates to informationprocessing, such as physical information processing, e.g., opticalinformation processing, using this interesting paradigm of reservoircomputing. Reservoir computing can find application in the analogdomain, e.g., for analog signal classification or for implementingnonlinear analog filters or controllers for which no closed formspecification is available, but also in the digital domain, e.g., forlearning boolean functions or automata, signal regeneration or headerrecognition.

Like many methods in this field, reservoir computing is partly inspiredby how the human brain works, but essentially, it is a method to usedynamical systems for computation. In reservoir computing, a dynamicalsystem, further referred to as the computing reservoir, is excited bythe inputs to be processed and its output states are trained to follow adesired output, e.g., by linear regression, while keeping the computingreservoir itself untrained. This is in contrast to recurrent neuralnetwork systems, which are notoriously difficult to train. The computingreservoir itself can be seen as a nonlinear pre-processor which projectsa time-variant input signal into a higher dimensional space where itbecomes easier to classify, e.g., using a linear classifier. For this,the reservoir is preferably in the proper dynamical regime at the edgeof instability, such that the system is dynamic enough without becominginstable. When feedback from the output to the reservoir is allowed, anyconceivable digital or analog computation on time-varying inputs, e.g.,in the idealized case without noise, can be carried out. Even withoutsuch feedback, any problem that requires fading memory, which forms abroad class of problems, can be solved under some general and mildconditions. Reservoir computing advantageously offers a system which iseasy to use, combined with computational capabilities matching orexceeding other state-of-the-art machine learning techniques for a broadrange of applications such as speech recognition, time seriesprediction, pattern classification and robotics. Due to the lenientrequirements for the computing reservoir, implementations have beendemonstrated in the art on diverse hardware platforms ranging from abasin of water to cellular neural networks and bacteria.

Software-based state-of-the-art implementations of reservoir computinghave in the recent past demonstrated good performance for a variety oftasks. However, dedicated hardware implementations may offer substantialspeed gains and power savings.

For example, a photonics-based hardware implementation of RC allows forfully exploiting the advantages offered by light, e.g., low power, highbandwidth and inherent parallelism, for computational purposes,especially when the input information is already encoded in the opticaldomain such as in many telecom applications or in image processing.Optical computing reservoirs, based on a fibre and a single dynamicalnode, are known in the art. Appeltant et al. disclosed such an approachin Nature Communications 2, article number 468. However, fibre-basedapproaches may have the disadvantages of being fairly bulky, being notstable enough to exploit information encoded in the phase component ofthe light, having a not very flexible interconnection topology andoffering poor scalability.

In other optical reservoir computing approaches known in the art,on-chip solutions with optical amplifiers have been used, for example asdisclosed by Vandoorne et al. in Optics Express 16(15), pp. 11182-11192.Here, it was shown that integrated optical chips with a network ofcoupled Semiconductor Optical Amplifiers (SOAs) can be used forreservoir computing. This offers the advantage of a small footprint andpermits the use of coherent light, such that a performance improvementcan be achieved over real-valued networks traditionally used in softwareimplementations as well as over fibre-based approaches. However, theintegrated optical chip disclosed by Vandoorne et al. may be not verypower efficient, e.g., due to the need for optical amplifiers.Furthermore, it requires a difficult technology, e.g., complexmanufacturing processes and relatively costly components. Furthermore,such approach may only offer a limited speed, e.g., fundamentallylimited by the carrier lifetime.

SUMMARY OF THE INVENTION

It is an object of embodiments of the present invention to provide goodand efficient reservoir computing based on optical systems.

It is an advantage of embodiments of the present invention thatversatile reservoir computing is provided, e.g., a single method and/ordevice according to embodiments can be suitable for a wide variety ofmachine learning tasks, e.g., for boolean function learning as well asspoken digit recognition.

It is an advantage of embodiments of the present invention that anoptical computing reservoir is provided, e.g., a passive siliconphotonics reservoir chip, which consumes substantially zero power, e.g.,does not require energy input except for providing the input andacquiring the output.

It is an advantage of embodiments of the present invention, that phaseinformation encoded in a wave-like physical phenomenon, can be exploitedfor reservoir computing operations, e.g., in addition to amplitudeinformation encoded therein.

It is an advantage of embodiments of the present invention, that goodscalability to larger networks and higher bitrates can be achieved.

It is an advantage of embodiments of the present invention, that highbitrates can be achieved, e.g., in the 20 to 200 Gbit/s range.

The above objective is accomplished by a method and device according tothe present invention.

The present invention relates to a method for characterizing an inputsignal, the method comprising the steps of:

-   -   providing an input signal to at least one input node of a        computing reservoir by supplying at least one photonic wave to        the at least one input node and by temporally encoding the input        signal by modulating the at least one photonic wave as function        of the input signal,    -   propagating said at least one photonic wave via passive guided        or unguided propagation between discrete nodes of said computing        reservoir, each discrete node being adapted for passively        relaying the at least one photonic wave over the passive        interconnections connected thereto,    -   obtaining a plurality of readout signals, in which each readout        signal is determined by a non-linear relation to the at least        one photonic wave in at least one readout node of said computing        reservoir, and    -   combining said plurality of readout signals into an output        signal, said combining taking into account a plurality of        training parameters.

Obtaining the plurality of readout signals may comprise obtaining theplurality of readout signals, wherein each readout signal is determinedby an intensity, energy or power measurement of said at least onephotonic wave in the at least one readout node.

The method may further comprise training said training coefficients byproviding a plurality of training input signals to the at least oneinput node of the computing reservoir and determining said trainingparameters by evaluating a difference between the plurality of readoutsignals and reference output signals corresponding to the plurality oftraining input signals.

The present invention also relates to a computing reservoir device forcharacterizing an input signal, the computing reservoir devicecomprising a plurality of discrete nodes and a plurality of passiveinterconnections between these discrete nodes for propagating the atleast one photonic wave between the discrete nodes, in which eachdiscrete node is adapted for passively relaying the physical quantityover the interconnections connected thereto, the discrete nodescomprising:

-   -   at least one input node for receiving an input signal and        temporally encoding the input signal in the at least one        photonic wave on said at least one input node, and    -   at least one readout node for providing a plurality of readout        signals, in which each readout signal is determined by a        non-linear relation to said at least one photonic wave in the at        least one readout node.

The device further may comprise a processor for combining said pluralityof readout signals into an output signal, said combining taking intoaccount a plurality of training parameters.

At least a subset of said passive interconnections may form at least oneclosed loop to maintain at least a short-term memory of said at leastone photonic wave.

The passive interconnections may comprise a delay line for transmittingsaid at least one photonic wave with a predetermined delay.

At least a subset of said passive interconnections may imprint a regulargrid spatial structure on the computing reservoir device.

At least a subset of said interconnections may imprint a modular orstratified spatial structure on said computing reservoir device.

Each of said passive interconnections may provide a predetermined delayand/or attenuation of the at least one photonic wave when transferredvia said interconnection.

Said at least one photonic wave may be an at least partially coherentlight wave.

The plurality of discrete nodes may comprise passive optical splittersand/or optical combiners and said plurality of passive interconnectionscomprise optical waveguides and/or optical fibres.

The at least one input node may comprise an optical coupler forreceiving the input signal as a light wave coupled into the reservoircomputing device.

The at least one readout node may comprise an optical coupler forcoupling out the light wave from said at least one readout node to alight intensity meter for producing the at least one readout signal, orin which the at least one readout node comprises a light intensity meterfor producing a light intensity measurement at the at least one readoutnode as the at least one readout signal.

The computer reservoir device is a passive silicon photonics reservoir.

Particular and preferred aspects of the invention are set out in theaccompanying independent and dependent claims. Features from thedependent claims may be combined with features of the independent claimsand with features of other dependent claims as appropriate and notmerely as explicitly set out in the claims.

These and other aspects of the invention will be apparent from andelucidated with reference to the embodiment(s) described hereinafter.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 illustrates a method for reservoir computing according toembodiments of the present invention.

FIG. 2 illustrates a schematic representation of an exemplary deviceaccording to an embodiment of the present invention.

FIG. 3 shows a device according to a first exemplary embodiment of thepresent invention, whereby a design of a 16 node swirl passive reservoirin 4×4 configuration is shown overlain with the topology.

FIG. 4 shows the Error Rate for a 2 bit XOR task trained and tested onmeasured and simulated data in accordance with the first exemplaryembodiment of the present invention.

FIG. 5 shows results for the 2 bit XOR task with measured data for awide variety of bit pairs in the bit stream in accordance with the firstexemplary embodiment of the present invention.

FIG. 6 shows results for other Boolean tasks on the measured data inaccordance with the first exemplary embodiment of the present invention.The results for an operation and its negation are the same (e.g., ANDversus NAND). Shown here are the results for x[−0] OPERATION x[−1](where x[−n] denotes the binary input value of n bit periods ago)although other bit combinations would also be possible.

FIG. 7 shows results for a 2 bit XOR task for one and two bits in thepast (x[−1] XOR x[−2]) in accordance with a first exemplary embodimentof the present invention. These results are grouped depending on thenonlinearity of the readout.

FIG. 8 shows simulation results for an isolated digit speech recognitiontask for coherent networks with three different node types in accordancewith embodiments of the present invention. Phase information was usedand the networks have the optimal delay selected for the speech task.

The drawings are only schematic and are non-limiting. In the drawings,the size of some of the elements may be exaggerated and not drawn onscale for illustrative purposes.

Any reference signs in the claims shall not be construed as limiting thescope.

In the different drawings, the same reference signs refer to the same oranalogous elements.

DETAILED DESCRIPTION OF ILLUSTRATIVE EMBODIMENTS

The present invention will be described with respect to particularembodiments and with reference to certain drawings but the invention isnot limited thereto but only by the claims. The drawings described areonly schematic and are non-limiting. In the drawings, the size of someof the elements may be exaggerated and not drawn on scale forillustrative purposes. The dimensions and the relative dimensions do notcorrespond to actual reductions to practice of the invention.

Furthermore, the terms first, second and the like in the description andin the claims, are used for distinguishing between similar elements andnot necessarily for describing a sequence, either temporally, spatially,in ranking or in any other manner. It is to be understood that the termsso used are interchangeable under appropriate circumstances and that theembodiments of the invention described herein are capable of operationin other sequences than described or illustrated herein.

Moreover, the terms top, bottom and the like in the description and theclaims are used for descriptive purposes and not necessarily fordescribing relative positions. It is to be understood that the terms soused are interchangeable under appropriate circumstances and that theembodiments of the invention described herein are capable of operationin other orientations than described or illustrated herein.

It is to be noticed that the term “comprising”, used in the claims,should not be interpreted as being restricted to the means listedthereafter; it does not exclude other elements or steps. It is thus tobe interpreted as specifying the presence of the stated features,integers, steps or components as referred to, but does not preclude thepresence or addition of one or more other features, integers, steps orcomponents, or groups thereof. Thus, the scope of the expression “adevice comprising means A and B” should not be limited to devicesconsisting only of components A and B. It means that with respect to thepresent invention, the only relevant components of the device are A andB.

Reference throughout this specification to “one embodiment” or “anembodiment” means that a particular feature, structure or characteristicdescribed in connection with the embodiment is included in at least oneembodiment of the present invention. Thus, appearances of the phrases“in one embodiment” or “in an embodiment” in various places throughoutthis specification are not necessarily all referring to the sameembodiment, but may. Furthermore, the particular features, structures orcharacteristics may be combined in any suitable manner, as would beapparent to one of ordinary skill in the art from this disclosure, inone or more embodiments.

Similarly it should be appreciated that in the description of exemplaryembodiments of the invention, various features of the invention aresometimes grouped together in a single embodiment, figure, ordescription thereof for the purpose of streamlining the disclosure andaiding in the understanding of one or more of the various inventiveaspects. This method of disclosure, however, is not to be interpreted asreflecting an intention that the claimed invention requires morefeatures than are expressly recited in each claim. Rather, as thefollowing claims reflect, inventive aspects lie in less than allfeatures of a single foregoing disclosed embodiment. Thus, the claimsfollowing the detailed description are hereby expressly incorporatedinto this detailed description, with each claim standing on its own as aseparate embodiment of this invention.

Furthermore, while some embodiments described herein include some butnot other features included in other embodiments, combinations offeatures of different embodiments are meant to be within the scope ofthe invention, and form different embodiments, as would be understood bythose in the art. For example, in the following claims, any of theclaimed embodiments can be used in any combination.

In the description provided herein, numerous specific details are setforth. However, it is understood that embodiments of the invention maybe practiced without these specific details. In other instances,well-known methods, structures and techniques have not been shown indetail in order not to obscure an understanding of this description.

In a first aspect, the present invention relates to a method forcharacterizing an input signal, e.g., for classifying the input signalin predetermined classes, for clustering the input signal or forproviding an estimate of a corresponding output signal, such as forobtaining a regression output. Therefore, a method according toembodiments of the first aspect may for example be suitable for signalrecognition, for estimating latent variables or unobserved outputvariables or for time series forecasting.

Referring to FIG. 1, an exemplary method 10 according to embodiments ofthe present invention is shown. This method comprises providing 11 aninput signal to at least one input node of a computing reservoir, inwhich the input signal is temporally encoded in at least one photonicwave on the at least one input node, e.g., in a photonic wave or aphysical property thereof at the at least one input node. The photonicwave or a property thereof may be quantifiable by measurement, e.g., canbe represented as a number and a reference, the number being related tothe input signal at the at least one input node.

Providing 11 the input signal to the at least one input node of thecomputing reservoir may comprise temporally encoding the input signal ina photonic wave. Thus, the physical quantity may be for example a lightwave.

The input signal may for example be temporally encoded in such aphotonic wave by modulating it. Temporally encoding the input signal inthe photonic wave may thus comprise changing a property of a wave at theat least one input node, e.g., changing an amplitude, phase, intensity,frequency or polarization property of a wave. It is an advantage of suchphysical quantities that the input signal may be encoded in acomplex-valued quantity, e.g., in a physical quantity having both a realand imaginary component. For example, such physical quantity may berepresented by phase and amplitude components, which jointly propagatethrough the computing reservoir in a wave-like manner. For example,providing 11 the input signal to the at least one input node of thecomputing reservoir thus may comprise supplying at least one photonicwave to the at least one input node, in which this at least one photonicwave is modulated as function of the input signal.

Providing 11 the input signal also may comprise receiving a photonicwave that is modulated as function of a signal from another photoniccomponent used for transferring or processing a signal.

The computing reservoir may be a passive system in which the physicalquantity is split and recombined in discrete nodes in a linear manner.With the physical quantity being a photonic wave, this passive systemmay still allow for complex, non-linear processing due to a nonlinearity in the readout. Thus, the system may provide complex dynamicalbehaviour, e.g., can be maintained in a nearly-instable state, withoutrequiring powered components such as amplifiers, provided the losses aresmall. The latter may result in a significant reduction in power used bythe system, as well as in significant less effort being required formanufacturing the device.

The method 10 further comprises propagating 12 the photonic wave via aplurality of passive interconnections between discrete nodes of thecomputing reservoir. For example, the computing reservoir may comprise aplurality of discrete nodes, e.g., which may comprise mechanicalresonators or optical splitters, for example, a number N of discretenodes, in which N is in the range of 1 to 1000000, e.g., in the range of10 to 10000, or in the range of 20 to 1000, for example 50 discreteunits or 200 discrete units. Where reference is made to discrete units,physical bodies adapted for splitting and/or combining the photonic wavesupplied via a predetermined set of passive interconnections are meant,e.g., manufactured units having a clearly defined structure. This is incontrast to, for example, elements of a continuous medium such as afluid or units which lack a clearly defined stable form or structure,e.g., a manufactured structure, such as magnetic domains in aferromagnetic material. Alternatively, continuous media can also bedealt with by evaluating them in a plurality of discrete points at theirsurface.

Each discrete node in this computing reservoir is adapted for passivelyrelaying the photonic wave over the interconnections connected thereto.For example, the passive interconnections may comprise photonic waveconductors such as optical fibres or optical waveguides.

The discrete nodes may for example be adapted for receiving the physicalquantity, e.g., photonic wave, from at least one interconnectionconnected thereto as a node input, and transmitting the physical thephotonic wave to at least one interconnection connected thereto as anode output. For example, the discrete node may passively combine thephotonic wave received from the node inputs, e.g., perform a complexsummation of the inputs, and distribute the combined photonic wave overthe output interconnections. The discrete node may therefore comprisefor example an optical beam splitter. The discrete node may have atleast three interconnections connected thereto, e.g., to perform atleast an additive combination of two inputs to one output or a passivesplitting of one input to two outputs. While splitting and combining ofthe physical quantity at the discrete nodes is, in accordance withembodiments of the present invention, a substantially passive process,e.g., does not add energy to the propagating photonic wave which was notreceived though this propagating photonic wave, the splitting andcombining may be performed using non-uniform weights. For example, whilein a discrete node according to some embodiments two inputs Z₁,Z₂ may besimply added to form a complex output Z=Z₁+Z₂, in a discrete node atleast one of the inputs Z₁,Z₂ may also be attenuated, e.g. phaseshifted, before addition, e.g., Z=Z₁+a·Z₂ with |a|≦1, a≠1 and a≠0.

The method 10 further comprises obtaining 13 a plurality of readoutsignals, in which each readout signal is determined by a non-linearrelation to the photonic wave in at least one readout node of thecomputing reservoir. This non-linear relation may for example be asquare, power, polynomial or root transformation of the photonic wave.In advantageous embodiments of the present invention, the non-lineartransformation may be an intensity or power measurement. For example,the photonic wave may have an amplitude-phase representation at thereadout node, where the readout signal or a component of the readoutsignal is determined as an intensity, energy or power measurement of thephotonic wave.

The readout values may be obtained simultaneously at a plurality ofreadout nodes of the computing reservoir, but may also be obtained bysampling at a plurality of readout nodes or at a single readout node,e.g., by obtaining readout values at different time instants at thereadout node or readout nodes. The readout values may also be obtainedby performing different non-linear transformations simultaneously at asingle readout node, e.g., applying a series of non-lineartransformations, e.g., a set of polynomial, exponential, root,trigonometric or other non-linear expressions.

The method 10 further comprises combining 14 the plurality of readoutsignals into an output signal, said combining taking into account aplurality of training parameters.

The method 10 may further comprise training these training coefficientsby providing a plurality of training input signals to the at least oneinput node of the computing reservoir and determining the trainingparameters by evaluating a difference between the plurality of readoutsignals and reference output signals corresponding to the plurality oftraining input signals. For example, training the training coefficientsmay be performed in accordance with a supervised learning technique,e.g., as known in the art for training reservoir computing outputweights. For example, output-error-minimizing weights may be computed.For example, teacher signals may be presented to the network, thereadout signals of the readout units may be mapped on the teacheroutput, optionally discarding a first set of input/readout pairs foraccommodating initial transient effects, and the weights of the readoutsignals for providing an appropriate output signal may be determined bya standard linear regression method. Alternatively, an online learningprocess also could be used, whereby input signals are continuously or inbatch provided to the at least one input nod of the computing reservoirand whereby the weights are gradually corrected based on theinstantaneous error that is detected, e.g., based on the estimatedsensitivity of these weights to errors.

Other steps may be added as will be apparent to the skilled person, inaccordance with reservoir computing methods as known in the art. Forexample, during training, noise may be inserted into the reservoirdynamics, e.g., by adding noise on the input and/or by adding a noisecomponent to the teacher output, in order to improve robustness of thecomputing reservoir output. The latter typically is referred to asregularisation.

As a method according to a first exemplary embodiment, a method 10 forcharacterizing an input signal is disclosed which makes use ofelectromagnetic waves, e.g., of coherent or partially coherent light,such as generated by a laser or a light emitting diode (LED) withpinhole collimation. Such method may comprise the steps of providing 11an input signal to at least one input node of a computing reservoir,e.g., to an optical coupler for coupling light into an integratedphotonic computing reservoir chip, by temporally encoding the inputsignal in an electromagnetic wave, e.g., in an at least partiallycoherent light wave, on the at least one input node, e.g., coupled intothe optical coupler.

The method may further comprise propagating 12 the electromagnetic wavevia a plurality of passive interconnections, e.g., integrated opticalwaveguides on the integrated photonic computing reservoir chip, betweendiscrete nodes of the computing reservoir. Each discrete node may beadapted for passively relaying the electromagnetic wave over the passiveinterconnections connected thereto. For example, the discrete nodes maycomprise integrated beam splitters and/or integrated beam combiners. Thediscrete nodes may be connected to at least one incoming passiveinterconnection for receiving at least one incoming electromagneticwave, which may be combined, e.g., for more than one incoming passiveinterconnection, and relayed to an outgoing passive interconnection ordistributed over a plurality of outgoing passive interconnections.

The method may further comprise obtaining 13 a plurality of readoutsignals, in which each readout signal is determined by a non-linearrelation to the electromagnetic wave in at least one readout node of thecomputing reservoir, e.g., the intensity or power of the electromagneticwave at at least one readout node may be determined through ameasurement device. For example, each readout node may be an integratedphotonic intensity or power meter or an integrated coupler for couplingthe electromagnetic wave into an output waveguide or fiber which has anintensity or power meter connected thereto.

The method may further comprise combining 14 the plurality of readoutsignals into an output signal, in which this combining takes a pluralityof training parameters into account. For example in a learning phase,the training parameters, e.g., linear regression coefficients, may havebeen determined for matching a combination, e.g., a linear combination,of the readout signals corresponding to specific input signals providedto the reservoir to corresponding specific target output signals.

In a second aspect, the present invention relates to a computingreservoir device for characterizing an input signal. Such computingreservoir device comprises a plurality of discrete nodes and a pluralityof passive interconnections between these discrete nodes for propagatinga photonic wave between the discrete nodes. Each of these discrete nodesis adapted for passively relaying the photonic wave over theinterconnections connected thereto. The discrete nodes comprise at leastone input node for receiving an input signal and temporally encoding theinput signal in the photonic wave on the at least one input node, thediscrete nodes also comprise at least one readout node for providing aplurality of readout signals, in which each readout signal is determinedby a non-linear relation to the photonic wave in the at least onereadout node. The computing reservoir device may also comprise aprocessor for combining the plurality of readout signals into an outputsignal. This combining furthermore takes into account a plurality oftraining parameters.

Referring to FIG. 2, an exemplary computing reservoir device 20according to embodiments of the second aspect of the present inventionis shown. This computing reservoir device 20 comprises a plurality ofdiscrete nodes 22 and a plurality of passive interconnections 23 betweenthese discrete nodes 22 for propagating a photonic wave between thediscrete nodes, in which each discrete node is adapted for passivelyrelaying the photonic wave over the interconnections connected thereto.

The plurality of passive interconnections, or a subset of the pluralityof interconnections 23, may form at least one closed loop to maintain atleast a short-term memory of the photonic wave, e.g., at least someinterconnections may form a feedback loop involving at least one of thediscrete nodes along this loop. Therefore, the photonic wave may berecombined with previous states of the photonic wave, e.g., withattenuated previous states such that a fading memory effect is achieved.Since the interconnections 23 and discrete nodes 22 are essentiallypassive, this attenuation may occur in a natural fashion, e.g., throughdispersion and decohesion of waves, propagation loss, or in anengineered fashion, e.g., due to purposeful passive attenuators in atleast some of the discrete nodes or interconnections.

The passive interconnections 23 may also comprise at least one delayline for transmitting the photonic wave with a predetermined delay, forexample, to scale the response of the computing reservoir device withthe speed at which input signals are provided thereto and/or readoutsignals are acquired and processed. Such optical delay lines, may alsoassist in obtaining a desired memory effect in the computing reservoirdevice 20, as will be understood by the skilled person.

At least a subset of the passive interconnections 23 may imprint aregular grid spatial structure on the computing reservoir device 20.Alternatively or additionally, at least a subset of the interconnectionsmay imprint a modular or stratified spatial structure on the computingreservoir device 20.

The discrete nodes 22 also comprise at least one input node 21 forreceiving an input signal and temporally encoding the input signal inthe photonic wave on the at least one input node 21. For example, thisat least one input node 21 may comprise an optical coupler for receivingan input light wave and relaying this input light to the computingreservoir via the input node, a light source, such as a led or laser forreceiving the input signal as a control current and sending a coherentor partially coherent light wave via the input node through thecomputing reservoir.

The discrete nodes 22 also comprise at least one readout node 24 forproviding a plurality of readout signals, in which each readout signalis determined by a non-linear relation to the photonic wave in the atleast one readout node.

The at least one readout node 24 may have no output interconnections,e.g., none of the passive interconnections 23 may receive an input fromthe at least one readout node 24 for relaying the photonic wave from theat least one readout node 24 back to another discrete node 22.Therefore, after training of the computing reservoir device, asubstantially passive signal processing network may be obtained.

However, in different embodiments, the at least one readout node 24 mayhave at least one of the passive interconnections 23 connected as outputinterconnection thereto for feeding back the photonic wave to at leastone discrete node 22 of the computing reservoir device, such that anactive signal processing or signal generation network may be obtainedafter training.

The reservoir computing device 20 further may comprise a processor 25for combining the plurality of readout signals into an output signal, inwhich this combining takes a plurality of training parameters intoaccount.

In the examples hereinbelow, experimental results and simulations areprovided for demonstrating the suitability of an integrated passivesilicon photonics chip according to embodiments of the present inventionfor use as a computing reservoir. Thanks to the reservoir computingparadigm, the same generic architecture can be used to calculatearbitrary boolean logic operations with memory up to 12.5 Gbit/s, aswell as for performing isolated spoken digit recognition. Apart from theversatility, other advantages of a passive silicon photonics reservoirchip are zero power consumption, e.g., except at inputs and outputs, theability to exploit phase for reservoir operations and excellentscalability to larger networks and higher bitrates. For example, 20 to200 Gbit/s may be trivially possible by eliminating the on-chip delaylines discussed below. In this example, artificial delay lines wereincluded on the integrated photonic chip device in order to slow it downsufficiently so as to be measurable with commonly available equipment.However, to make this compatible with high-speed systems, the delaylines need simply to be shortened or eliminated altogether. Embodimentsof the present invention can therefore provide useful integratedphotonic reservoir computing for a wide range of applications.

The reservoir computing device according to this particular examplecomprises a passive optical network, e.g., consisting of onlywaveguides, splitters, combiners and/or other passive optical elements,and does not contain non-linear elements except at the readout stage.The non-linearity may be created at the readout level, where the complexamplitudes are converted into real-valued powers, e.g., light intensitymeasurements. Thus, the nonlinearity, assumed to be a desirable propertyaccording to previous work in the art, is no longer present in thereservoir itself, but is rather implemented at the readout by convertingthe complex amplitudes of the photonic waves propagating through thereservoir nodes into real-valued power levels. The readout signalsobtained through this non-linear relation may then be used as input fora linear classifier. In this way, the reservoir itself consumes zeropower, and its timescale is determined by the interconnection delaybetween nodes. In exemplary chip discussed here, 2 cm delay spirals wereused to bring this speed down to a range of 0.125-12.5 Gbit/s, but bytrivially eliminating these delay lines speeds up to 5-500 Gbit/s, e.g.,corresponding to a 40 times reduction resulting in interconnections downto 500 μm, may be obtained. A further reduction to allow for even fasterspeeds (e.g., with interconnections of 200 μm) may require someredesigning of the exemplary reservoir design discussed here, e.g., toachieve an extremely compact footprint. This redesigning can beperformed using ordinary skill in the art, as willed be understood bythe skilled person.

Such a passive nanophotonic silicon reservoir can be used as a genericcomputational platform for diverse tasks, both digital and analog.Experimental results provided further hereinbelow demonstrate that thechip is capable of performing arbitrary Boolean logic operations withmemory on a time stream, like x[−2] XOR x[−3], or x[−1] NAND x[−2],where x[−n] is the input n bits in the past. Furthermore, goodcorrespondence is achieved between simulation and experiment.

It is also demonstrated by the simulation results hereinbelow that thesame chip is capable of performing a high-speed analog task, namely thatof isolated spoken digit recognition.

The exemplary chip design for this example is shown in FIG. 3, whichshows a 16 node reservoir having a 4-by-4 so-called “swirl” topology,which creates feedback loops in the network. Underneath, the actual chipdesign is visible and the connections 23 consist of 2 cm long low-lossspirals 31 (1.2 dB loss per spiral) corresponding with aninterconnection delay of around 280 ps. These delay lines have the solepurpose of slowing down the reservoir such that it becomes accessiblewith commonly available experimental equipment.

All shown connections are essentially bidirectional, but by using oneinput 21 the light flows according to the overlain arrows. Readouts wereobtained at the 11 nodes marked with a full dot were measured.

Indeed, as the network is passive, the timescales that matter are thespeed of the signal itself and the interconnection time delays.Therefore, the reservoir was also studied as a function of the delay/bitperiod ratio. A small/high ratio means that the signal is slow/fastrelative to the network connections. The measurement equipment for thisexample allowed to scan bitrates between 125 Mbit/s and 12.5 Gbit/s,which corresponds to a range of situations where the delay is only afraction of the bit period to situations where the delay is a multipleof the bit period.

The footprint of the exemplary reservoir chip is 16 mm², mostly becauseof the size of the spirals. To ensure low losses, these spirals wereshallow etched waveguides with a bending radius of 40 nm. A chip withshorter interconnections for higher speeds would allow using spiralswith deep etched waveguides. This may be lossier, but provides a smallerfootprint as the bending radius is around 5 nm (1.36 dB/cm versus 0.3dB/cm), allowing for an even greater size reduction.

Coupling and splitting between the nodes is done with a combination of1×2 and 2×2 Multi-Mode Interferometers (MMI) with very low insertionloss and broadband operation over the wavelength range of the gratingcouplers used to couple light on and off chip. The loss per gratingcoupler is 5-6 dB. The chip is made on a Silicon-on-Insulator platform(SOI) (www.epixfab.eu), which uses the manufacturing tools from thesemiconductor electronics industry. This holds the promise for massproduction at low cost and the high-index contrast of SOI allows for amuch smaller footprint than what is possible in other materialplatforms.

The passive reservoir was fabricated on a Silicon-on-Insulator waferwith 193 nm DUV lithography. The SOI structure was designed with a topsilicon layer of 220 nm and a buried oxide layer of 2 mm.

Making active components in SOI is a topic of ongoing research assilicon has an indirect bandgap, but as the presented exemplaryreservoir according to embodiments of the present invention is passive,one can take full advantage of the maturity of silicon processingtechnology.

The coupling to and from the chip was performed with a vertical fibresetup.

In a first example of measurement and simulation relating to a Booleantask, 10000 bits were divided into 10 sets of 1000 bits used in turn fortraining and testing through 5-fold cross-validation and ridgeregression to avoid over-fitting. The pattern of 10000 bits wasgenerated with an Anritsu MP2101A Pulse Pattern Generator and themeasured signal was first amplified with a Keopsys EDFA, then filteredand finally detected with a LeCroy WaveExpert 100H.

After training the readout weights on the training bit stream, both thetested output (which consists of applying those weights to the states ofthe reservoir of the test bit stream) and desired output are sampled atthe middle of the bit period and thresholded at the middle of the bitamplitude. These two bit streams are then compared to determine theperformance of the system, yielding an error rate. The desired bitstream is constructed from the input bit stream depending on the Booleanoperation that needs to be solved. The 11 measured reservoir states arepadded initially with zeros depending on the signal frequency and thephysical interconnection distance from the input node in FIG. 3.

An optical stream of 10000 bits, modulated on a wavelength of 1531 nm atthe maximum transmission of the grating couplers, were sent into theinput node 21 of the chip, and the response was measured at the elevenreadout nodes 24 marked with a filled-in dot on FIG. 3. The other 5nodes had output powers below the noise floor (±−40 dBm or 100 nW) ofthe Erbium-Doped Fiber Amplifier (EDFA) used for this example. However,more nodes may be measured by amplifying the input signal and by usingmore efficient couplers to and from the chip. The amplified responseswere measured with an optical sampling scope and saved to a computerwhere they were used for offline training with a freely availabletoolbox. The measured states are trained to follow a certain desiredoutput, e.g., the XOR of the present bit and the previous bit, and thedifference between the trained output and the desired output gives theError Rate (ER).

FIG. 4 shows that for a 0.14 delay/bit period ratio a good performanceis achieved for the XOR of the present and previous bit. The plots showa first graph 33 for x−0 XOR x−1 and a second graph 34 for x−3 XOR x−4.

The network was also simulated, which produced a similar response, apartfrom the local minimum of 25% at a 0.5 delay/bit period ratio that wasobtained for the simulated network. The simulated results are shown withdashed interconnecting lines, while the experimental results are shownwith full interconnecting lines on FIG. 4.

Note that despite its apparently simplicity, this XOR task with memoryis considered to be a hard problem in machine learning, as it cannot besolved by mere linear regression on the inputs, but a result of 25% is,however, possible as a suboptimal solution, e.g., in this case one ofthe four solutions is constantly misclassified. Also, for the XOR of thethird and fourth bit in the past, a good agreement between measurementand experiment is obtained, albeit at slightly different delay/bitperiod ratios. This may be likely caused by small differences betweenthe simulated reservoir and the one actually fabricated.

It may be important to note that the generic network, which was not atall specially optimized and designed for a 2 bit XOR with one bit delay,can solve the XOR of many different bit combinations, as illustrated byFIG. 5, and other Boolean operations, as illustrated by FIG. 6,demonstrating the general applicability of the RC paradigm. Since theoptimum exists for certain delay/bit period ratios, chips can easily bedesigned to handle very high speeds. For example, a signal of 100 Gbit/srequiring a ratio of 0.5 needs a delay of 50 ps (±0.5 mm), which isperfectly feasible. The optimal delay/bit period range for the differenttasks in FIG. 6 is 0.14-1.4 and in case the connections are shortened to500 μm, this leads to a theoretical optimal bitrate range of 20-200Gbit/s.

The nonlinearity present in this system is further investigatedhereinbelow, as reservoirs usually need some kind of nonlinearity tosolve nonlinear tasks (the XOR being one of them). As mentioned before,the reservoir in accordance with embodiments of the present invention ispassive, and there is no apparent nonlinearity to be found there.However, light detectors measure intensity, which means that the squareis taken from the absolute value of the complex amplitude of coherentlight. This operation matters as can be seen in the simulation resultsof FIG. 7. Linear readouts are not capable of solving the x−1 XOR x−2task. However, as soon as there is a polynomial functionality in thereadout, as for example happens in a real photodetector, the taskbecomes solvable.

Linear operations such as utilizing a complex readout with complexweights working directly on the complex amplitude, e.g., linear in thecomplex plane, or using only optical powers in the reservoir, e.g.,without phase information and thus incoherent light, yield a very badperformance for the XOR task. However, as soon as there is a kind ofpolynomial nonlinearity in the detection, e.g., the absolute value ofthe complex amplitude or the square of it as in standard detectors, theperformance is good. When only the phase information is used, anonlinear operation itself, the performance is somewhere in between.This means that the easiest approach to detecting the photonic states,employing normal photodetectors, may also be the most powerful for RC.The phase information does not need to be extracted separately as it isalready captured in the interference effects seen in the intensities. Inthe present example, the readout and linear regression was stillimplemented in the electrical domain. However, it is conceptual easy toalso implement this linear combination of states in the optical domain,as will be apparent to the person skilled in the art, where a set ofmodulators or amplifiers implement the weights. In this case, however,the nonlinear operation would be performed after taking the weighted sumin the complex domain, requiring a more complex training procedure thatthe common linear regression.

In a second exemplary task, isolated spoken digits, ‘zero’ to ‘nine’,were classified. In the data set, these words are each spoken 10 timesby 5 female speakers, giving 500 samples, taken from the TI46 speechcorpus. For speech recognition, some pre-processing of the raw speechsignal is commonly performed. These methods often involve atransformation to the frequency domain and a selective filtering basedon known psycho-acoustic properties of the human ear and/or spectralproperties of speech. To shorten the simulation time, a decimation ofthe input signals with a factor of 128 was also applied. The output wasobtained by training ten distinct linear classifiers, one for eachdigit. Each trained output should return the value +1 whenever thecorresponding digit is spoken and −1 otherwise. During testing, awinner-take-all approach was used to determine which word was spoken.The word error rate (WER), which is (N_(nc)/N_(tot)), with N_(nc) thenumber of incorrectly classified samples, and N_(tot) the total numberof samples, determines the performance. Since it is possible to achievea WER very close to 0%, babble noise from the NOISEX database was addedwith a SNR of 3 dB. The results are always averaged over 10 runs. Ridgeregression was used to avoid over-fitting and five-fold cross-validationwas used to make the results more robust.

The most important properties of photonic reservoirs in general by meansof simulations for an isolated digit recognition task were alreadystudied in Vandoorne et al. in IEEE Transactions on Neural Networks22(9), pp 1460-1481 discussed in the background section hereinabove. Thereservoir employed there was a network of coupled SOAs and by working atan optimal delay and in the coherent regime, better results than withclassical real-valued reservoirs in software were achieved. FIG. 8 showsthat the same kind of performance can also be achieved by replacing theSOA chip with the passive silicon network as used in the digital taskexample hereinabove. Since no high-speed analog arbitrary waveformgenerator was readily available, this was not tested experimentally, butthe good correspondence between theory and experiment for the digitaltask leads to the conclusion that the same architecture can also be usedfor solving analog problems.

The invention claimed is:
 1. A method for characterizing an inputsignal, the method comprising the steps of: providing an input signal toat least one input node of a computing reservoir by supplying at leastone photonic wave to the at least one input node and by temporallyencoding the input signal by modulating the at least one photonic waveas function of the input signal, propagating said at least one photonicwave via passive guided or unguided propagation between discrete nodesof said computing reservoir, each discrete node being adapted forpassively relaying the at least one photonic wave over the passiveinterconnections connected thereto, obtaining a plurality of readoutsignals, in which each readout signal is determined by a non-linearrelation to the at least one photonic wave in at least one readout nodeof said computing reservoir, and combining said plurality of readoutsignals into an output signal, said combining taking into account aplurality of training parameters.
 2. The method according to claim 1, inwhich obtaining the plurality of readout signals comprises obtaining theplurality of readout signals, wherein each readout signal is determinedby an intensity, energy or power measurement of said at least onephotonic wave in the at least one readout node.
 3. The method accordingto claim 1, further comprising training said training coefficients byproviding a plurality of training input signals to the at least oneinput node of the computing reservoir and determining said trainingparameters by evaluating a difference between the plurality of readoutsignals and reference output signals corresponding to the plurality oftraining input signals.
 4. A computing reservoir device forcharacterizing an input signal, the computing reservoir devicecomprising a plurality of discrete nodes and a plurality of passiveinterconnections between these discrete nodes for propagating the atleast one photonic wave between the discrete nodes, in which eachdiscrete node is adapted for passively relaying the at least onephotonic wave over the interconnections connected thereto, the discretenodes comprising: at least one input node configured for receiving aninput signal and temporally encoding the input signal in the at leastone photonic wave on said at least one input node, and at least onereadout node configured for providing a plurality of readout signals, inwhich each readout signal is determined by a non-linear relation to saidat least one photonic wave in the at least one readout node, the devicefurther comprising a processor programmed for combining said pluralityof readout signals into an output signal, said combining taking intoaccount a plurality of training parameters.
 5. The device according toclaim 4, in which at least a subset of said passive interconnectionsform at least one closed loop to maintain at least a short-term memoryof said at least one photonic wave.
 6. The device according to claim 4,in which the passive interconnections comprise a delay line fortransmitting said at least one photonic wave with a predetermined delay.7. The device according to claim 4, in which at least a subset of saidpassive interconnections imprint a regular grid spatial structure on thecomputing reservoir device.
 8. The device according to claim 4, in whichat least a subset of said interconnections imprint a modular orstratified spatial structure on said computing reservoir device.
 9. Thedevice according to claim 4, in which each of said passiveinterconnections provide a predetermined delay and/or attenuation of theat least one photonic wave when transferred via said interconnection.10. The device according to claim 4, in which said at least one photonicwave is an at least partially coherent light wave.
 11. The deviceaccording to claim 4, in which the plurality of discrete nodes comprisepassive optical splitters and/or optical combiners and said plurality ofpassive interconnections comprise optical waveguides and/or opticalfibres.
 12. The device according to claim 4, in which the at least oneinput node comprises an optical coupler for receiving the input signalas a light wave coupled into the reservoir computing device.
 13. Thedevice according to claim 4, in which the at least one readout nodecomprises an optical coupler for coupling out the light wave from saidat least one readout node to a light intensity meter for producing theat least one readout signal, or in which the at least one readout nodecomprises a light intensity meter for producing a light intensitymeasurement at the at least one readout node as the at least one readoutsignal.
 14. The device according to claim 4, wherein the computerreservoir device is a passive silicon photonics reservoir.